The goals of this research are to bring new implicit polynomial 2D curve and 3D surface object recognition concepts to a state of general usefulness to researchers in computer vision and image processing, and to develop computationally-fast shape-based indexing into 2D image and 3D image databases. The approaches to be used include new fitting concepts and algorithms, new types of invariants, new concepts and algorithms for single-computation pose estimation for implicit polynomial 2D curves and 3D surfaces, and indexing by matching rich sets of 2D curvelets or rich sets of 3D surface patchlets with those that have been autonomously extracted and stored in the image databases. This work will assess the value of implicit polynomial methods for modeling and making inferences about object shape in 2D and 3D data. The research will also produce useful tools for the research community for applications, and will provide an understanding of the strengths and weaknesses of this technology. Searching and indexing into image databases is a rapidly growing activity in science and commerce. This project will provide an understanding of the geometric shape-based indexing accuracy and speed and the automation of database preparation possible with the new implicit polynomial methodology.
